Most fracture mechanics analysis is based on the assumptions of prefabricated crack and ideal undamaged body. In practical, a cracked structure contains microstructural defects so that the material damage is considered to exist in the body rather than an ideal defect-free body. In this paper, it is the first time to take the material damage into account to the constitutive equation of quasicrystals, and the anti-plane fracture analysis of the one-dimensional hexagonal piezoelectric quasicrystals is carried out to obtain the more actual solutions. The continuum damage mechanics theory is used to define the damage variable and evolution law of the micro-voids’ growth in the quasicrystals. Semi-qualitative analysis of damage effects on the stress intensity factors are conducted, in which the stress intensity factors and J-integral are solved by using the boundary element method. In a case study, the fields of stress and displacement along the crack or distributed on the plate are obtained. The comparisons between the presented numerical results and the analytical results have good agreement, which verifies the accuracy of the presented solutions. The numerical results suggest that fracture failure analysis for quasicrystals engineering applications should consider the effective (actual) stress intensity factors calculated by the effective stress instead of nominal stress intensity factors.

大多数断裂力学分析是基于预制裂纹和理想的未损坏车身的假设进行的。实际上，破裂的结构包含微结构缺陷，因此材料损伤被认为存在于体内，而不是理想的无缺陷的体内。本文是首次将材料损伤考虑到准晶体的本构方程中，并对一维六角形压电准晶体进行了抗平面断裂分析，以获得更实际的解决方案。连续损伤力学理论用于定义准晶体中微孔生长的损伤变量和演化规律。对损伤对应力强度因子的影响进行了半定性分析，采用边界元法求解应力强度因子和J积分。在一个案例研究中，获得了沿着裂纹或分布在板上的应力和位移场。数值结果与解析结果的比较吻合良好，验证了所提方法的准确性。数值结果表明，准晶体工程应用中的断裂破坏分析应考虑通过有效应力计算的有效（实际）应力强度因子，而不是名义应力强度因子。数值结果与解析结果的比较吻合良好，验证了所提方法的准确性。数值结果表明，准晶体工程应用中的断裂破坏分析应考虑通过有效应力计算的有效（实际）应力强度因子，而不是名义应力强度因子。数值结果与解析结果的比较吻合良好，验证了所提方法的准确性。数值结果表明，准晶体工程应用中的断裂破坏分析应考虑通过有效应力计算的有效（实际）应力强度因子，而不是名义应力强度因子。